ModelFitting

Modelfitting is the process of selecting a mathematical model to describe relationships among variables and estimating its parameters from data. The aim is a model that summarizes the data-generating process while remaining interpretable and generalizable to new observations.

Common approaches include frequentist estimation (least squares for linear models and maximum likelihood for many distributions) and Bayesian methods that yield a posterior over parameters. Regularization, such as ridge and lasso, addresses overfitting in high-dimensional settings. Nonlinear and probabilistic models, including generalized linear and hierarchical models, broaden the range of describable relationships.

Model fit is assessed with diagnostics and predictive performance. Residual analysis, information criteria (AIC/BIC), and cross-validation gauge fit and generalization.

Typical workflows include choosing a model class, preprocessing data, estimating parameters, diagnosing fit, and comparing alternatives. Key considerations are identifiability, misspecification, overfitting, and data quality.

Modelfitting supports inference, forecasting, and decision making across disciplines. It relies on assumptions about the data-generating process and may not imply causality; interpretability and computational cost influence results.